X(x)(x)+y=y+x(x)(x)

Solution for X(x)(x)+y=y+x(x)(x) equation:

Simplifying
X(x)(x) + y = y + x(x)(x)

Multiply X * x
xX * x + y = y + x(x)(x)

Multiply xX * x
x2X + y = y + x(x)(x)

Multiply x * x
x2X + y = y + x2 * x

Multiply x2 * x
x2X + y = y + x3

Reorder the terms:
x2X + y = x3 + y

Add '-1y' to each side of the equation.
x2X + y + -1y = x3 + y + -1y

Combine like terms: y + -1y = 0
x2X + 0 = x3 + y + -1y
x2X = x3 + y + -1y

Combine like terms: y + -1y = 0
x2X = x3 + 0
x2X = x3

Solving
x2X = x3

Solving for variable 'x'.

Combine like terms: x3 + -1x3 = 0
x2X + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(X + -1x) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(X + -1x)' equal to zero and attempt to solve:

Simplifying
X + -1x = 0

Solving
X + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1X' to each side of the equation.
X + -1X + -1x = 0 + -1X

Combine like terms: X + -1X = 0
0 + -1x = 0 + -1X
-1x = 0 + -1X
Remove the zero:
-1x = -1X

Divide each side by '-1'.
x = X

Simplifying
x = X
Solution
x = {0, X}